Dimensional Analysis

Also called factor label method

Used to convert from one unit to another

• We learned the “King Henry” method for moving the decimal point when we were converting from one metric unit to another. That is the easiest way to change from one unit to another in the metric system, but you could use this method instead.

Dimensional analysis is based on the following principle: When you multiply a number by one, the number does not change.

For example:48 inches x 1 = 48 inches

48 inches x 12 = 48 inches 12

48 inches x 1foot = 48 inches 1foot

48 inches x 1foot = 48 inches 12 inches

In each example, 48 inches is multiplied by one.

We can use this principle to convert from one unit to another (ex. From inches to feet)

Step 1: Write the unit you want to change over 1

Step 2: Find a conversion factor that connects the old unit to the new unit

Step 3: Multiply the old unit times the conversion factor written as a fraction. When you write the fraction, make sure that the unit you are trying to get rid of is on the opposite side of the fraction.

Step 4: Cancel units that are the same on the top and bottom.

Step 5: Multiply the numerators; multiply the denominators; then simplify.

Example 1:

48 inches = _______ feet.

Step 1: Write the number over 1.

48 inches

1

Step 2: Find a conversion factor that connects one unit to the other.

1 foot = 12 inches

Step 3: Multiply the old unit times the conversion factor written as a fraction. Make sure the unit you want to get rid of is on the opposite side of the fraction.

48 inches x 1 foot

1 12 inches

Step 4: Cancel the unit that are the same on the top and bottom.

48 inches x 1 foot

1 12 inches

Step 5: Multiply the numerators; multiply the denominators; simplify

48 inches x 1 foot = 48 feet = 4 feet

1 12 inches 12

Written another way:

Starting units x Desired units = desired units

starting

•Example 1:

ex. Convert 750mL into L

Conversion factor: 1 L = 1000 mL

750mL x 1L

1 1000mL= 0.75 L

•Example 2:

ex. Convert 247.5g into cg

Conversion factor: 100 cg = 1 g

247.5g x 100cg

1 1g

= 24750 cg

Now, you try it:

7 days = ____ hours.

What would be your conversion factor?

How’d you do?

Conversion factor:

1 day = 24 hours

So…

7 days x 24 hours = 168 hours

1 1 day

Sometimes there’s more than one step involved….

• Ex: 5 days = ____ minutes

• You would need to find 2 conversion factors

• 1 day = 24 hours

• 1 hour = 60 minutes

5 days x 24 hours x 60 mins = 7200 mins

1 1 day 1 hour

You try:

.75 Hour = _____ seconds

Answer

Conversion factors

1 hour = 60 mins

1 min = 60 seconds

.75 hour x 60 mins x 60 secs = 2700 secs

1 1 hour 1 min